Stop Worshiping False Idols

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My response was, admittedly, merely reflecting our current sentiment and has no meaning outside of the milieu in which it is uttered.
Maybe our present milieu has it wrong or partially wrong? Or, if milieu is all there is, then the meaningfulness of the utterance is hopelessly contingent upon it. When the milieu changes, the truth will change with it. That's a radical thought, no?

Throughout history there have been grand proclamations about the death of metaphysics, but what we do not realize is that it is not the task of philosophy (and natural science as well if we were to heed Popper's advice) to prove or establish a certain worldview, but rather to show that certain worldviews are highly improbable or contradictory.
If a metaphysics can be demonstrated to fail the test of fidelity (probability) and/or coherence (contradictions), is that not a proof?



You seem to be positioning philosophy as a falsification game (e.g,. Popper's view of science), but the tasks of philosophy depend on the ambitions of the philosopher, right?



My take, and I speak with no particular authority, is that metaphysics is as vexing as it is inescapable. There is no anti-metaphysical stance (for that stance will itself assume its own metaphysical picture).

Hence my claim that "there are no (x) entities" should be read as a negation rather than a positive metaphysics. It's never about burden of proof, but the spirit of thinking involves bold conjectures and incessant attempts to show that the certain ideas implode on themselves if we were to postulate them as a positive metaphysics.
I don't think we can escape positive metaphysics. There is no "view from nowhere," no analysis/evaluation without assumptions.



When you say certain ideas implode on themselves, do you mean to imply that certain ideas do not? If so, there is hope for positive metaphysics. And if not, implosion is a "non-unique" liability. Everything falls apart upon close inspection held to the highest standards, and this would seem to deprive us of the ability to argue for nominalism or against idealism or whatever, right?

In fact, I am somewhat of an Idealist, believing in a form of mathematical platonism (without the capital P) which is different from substance Platonism implied by the original post of this thread.
Sounds agreeable to me. And I appreciate that even saying something like this requires a considerable amount of courage in some quarters.

Moreover, I'm also an Idealist in this regard - that Ideas matter and are both invented and discovered.
This seems to be the most reasonable take. Not to discount abstractions entirely (throwing out the baby with the bathwater), but not committing to reifying all abstractions as necessarily being substantive.

Even so we can all agree that the nature of numbers is quite radically different in kind than the nature of physical properties and attributes.
Different, perhaps. But what matters is that they have aspects which are substantive. And math "works" because we have been so very (unreasonably so, according to some) successful in correlating the ideas of mathematics with the physical world we perceive with our senses. Math and science are like peas and carrots, quite complementary.

And even if mathematical entities are indispensable (according to Quine), we still haven't establish a causal relationship between the two (mathematics and matter).
Would that be necessary or even desirable?

The fact that you bring up solipsism as a legitimate position already betrays the spirit of thinking in the first place. But why should we waste our time debating with solipsists, if their only strategy is to use a sleight of hand and shut down/block off all criteria, let alone agreeable grounds, for debate?
The point about solipsism is not that it is legitimate (in the sense that it deserves to be a leading position), but rather that it is not a position we can eliminate conclusively. And it is not that they use sleight of hand or shutdown criteria, but rather that we lack the resources to prove that the solipsist's position is decidedly wrong. Our reasons for rejecting solipsism are practical (e.g., the world is functionally no different if the solipsist is correct). I can't kick the solipsist out of the room, but that does not mean that I am passing her the microphone either.



I believe that there are depths. I'll grant that the depths are murky, but I don't know how to reason in a world with no depths (where its all sliding surfaces). I don't know how to proceed rationally without the law of identity or the excluded middle. I think that we have to treat abstract ideas with some respect, dangerous as they can be, because the dangers of full-on nominalism are just as dangerous.



Haha, indeed, the postmodern clown car appears ever so briefly and ferociously, thrilling us with its tantalizing repartee of esoteric etymologies and abstruse axioms. How jocundly droll, to precipitously embark on a protractive foray into eidetic metacognition, wherein we may muse upon the ontological existence of the multi-dimensional world and deconstruct the boundaries of solipsism with a synergetic diatribe of dialectic exegesis.
Yeah, yeah, or we can just pop some popcorn and do some munching.